Thermal transport in long-range interacting Fermi-Pasta-Ulam chains

Abstract

Studies of thermal transport in long-range (LR)interacting systems are currently particularly challenging. The main difficulties lie in the choice of boundary conditions and the definition of heat current when driving systems in an out-of-equilibrium state by the usual thermal reservoirs. Here, by employing a reverse type of thermal baths that can overcome such difficulties, we reveal the intrinsic features of thermal transport underlying a LR interacting Fermi-Pasta-Ulam chain. We find that under an appropriate range value of LR exponent $\sigma =2$, while a \emph{nonballistic} power-law length ($L$) divergence of thermal conductivity $\kappa$, i.e., $\kappa \sim L^{\alpha}$ still persists, its scaling exponent $\alpha \simeq 0.7$ can be much larger than the usual predictions in short-range interacting systems. The underlying mechanism is related to the system's new heat diffusion process, weaker nonintegrability and peculiar dynamics of traveling discrete breathers. Our results shed light on searching for low-dimensional materials supporting higher thermal conductivity by involving appropriate LR interactions.